= Solution
A suitable accelerator-science example is <strong focusing>. The apparent technical contradiction is that increasing a <quadrupole magnet>'s focusing strength improves confinement in one transverse plane while worsening it in the other. Abandoning that magnet entirely loses its strong focusing action.
An alternating-gradient lattice separates the two actions in space: a focusing quadrupole in one plane is followed, after a drift, by one with the opposite sign, and the pattern repeats. In the other plane their roles reverse. The symmetric thin-lens <FODO cell> has the same trace $2-d^2/f^2$ in both planes, so both are stable for $0<d/|f|<2$, despite each individual quadrupole defocusing one plane. The noncommuting sequence of drift and lens maps is what makes net confinement possible.
In a TRIZ interpretation, this resolves the contradiction by \b[spatial separation and periodic alternation] of opposing functions, rather than demanding that one static element satisfy both. The useful result is smaller beam envelopes and magnet apertures for a suitable lattice. This is a retrospective design analysis; it does not claim that the historical inventors actually followed TRIZ. The matrix calculation supplies a test of the proposed resolution rather than just attaching a slogan to an invention.
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